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I know a REC709 timeline is used for most deliverables in Resolve, but I was wondering what real advantages would one get from using REC2020? It's becoming more popular for 4k and HDR projects. I know most TV stuff is done in 8 bit, so REC709 is enough. But what about DCP for movie projection? I never graded in a REC2020 color space so I'm quite unfamiliar with whatever differences might exist...

The big difference is a much broader color gamut, well beyond what would clip in REC709. You would need a display solution, 10 bit video card or external HDSDI/ HDMI video encoder and an REC2020 rated true 10 bit display, even one of the newest high end OLED or HDR rated consumer TV's to be able to see what you are grading. REC2020 only applies to UHD TV formats.
REC2020 and REC709 are both display referenced color spaces, so if your grading display solution is only REC709 capable, that is what you are grading to as a reference even if you are working in a different color space.
Resolve lets you monitor and grade in REC709 but still deliver mathematically correct conversions to other color spaces like REC2020 or DCIP3, but your grades will only be visibly accurate for the range of color values that fall within REC709 limits.

The big difference is a much broader color gamut, well beyond what would clip in REC709. You would need a display solution, 10 bit video card or external HDSDI/ HDMI video encoder and an REC2020 rated true 10 bit display, even one of the newest high end OLED or HDR rated consumer TV's to be able to see what you are grading. REC2020 only applies to UHD TV formats.
REC2020 and REC709 are both display referenced color spaces, so if your grading display solution is only REC709 capable, that is what you are grading to as a reference even if you are working in a different color space.
Resolve lets you monitor and grade in REC709 but still deliver mathematically correct conversions to other color spaces like REC2020 or DCIP3, but your grades will only be visibly accurate for the range of color values that fall within REC709 limits.

Thanks for your informative post! One more question. My display is not a color grading tool so I doubt it will be able to do REC2020. My question is, how do I set the gamma on my display to be exactly 2.2 (which is the gamma value I use in Resolve for a REC709 timeline)? I tried a bunch of visual squares that a guy posted online, but never really understood how to calibrate based on that...

Gamma 2.2 is for sRGB which is what a lot of computer screens use. Rec.709 is supposed to be gamma 2.4. I grade in Resolve using gamma 2.4 and haven't had any complaints at least in regard to that. You TV may default to that gamma, but somewhere in the setup, you may find the choice of gamma. Or it may just say 'movie' versus standard or vibrant etc.

If you are creating deliverables for Cinema, then use DCI-P3 unless told otherwise. Your deliverables for the Internet could be something else, like sRGB, but for HDTV I think Rec.709 will suffice. Rec.2020 maybe on UHDTV, but not all 4K TVs are created equal. Very few license Dolby Vision that uses Rec.2020, but Visio is a 'budget' brand that has upped their game and does include Dolby Vision. Samsung won't pay Dolby any royalties as they're part of a consortium that developed their own standard after Dolby announced Dolby Vision. I have a Samsung HDTV, but it's the last one I'll buy. Next time it may be Visio UHDTV.

Why no love for Samsung? You can get a really good one for nothing. I had a Vizio once and the skin tones were horrid, you couldn't make it look good or accurate no matter how hard you tried. With a Samsung put contrast at 65, brightness at 43, everything else at 50 and you're good. The Dolby Vision "White Paper" is more marketing than science, those Ds cost money.